## Transmission line maximum impedance

• 3
Can a transmission line have characteristic impedance greater than free space (377 ohms?)

The wire over ground calculator impedance goes to infinity for infinite height... is that real, or is there a limit that needs to be enforced somehow?

https://www.microwaves101.com/calculators/874-wire-over-ground-calculator

Steve
• 0
I don't think so, but now I see you can buy 600 Ohm ladder line, so I don’t know. Skim through this, particularly section 5 where he looks at TM waves on two wires lines. The TM cutoff is lambda/2 wire separation, so it'd be lambda/4 for wire-over-ground if you treat it as an image. Really no different than microstrip.

What's more interesting is the TE mode for really large wire diameters, but that's expected as it's in microstrip too.

I'd just add a disclaimer saying it's for TEM only.

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiOt6Cd4PvuAhUWbs0KHVBKBKAQFjAAegQIBRAD&url=http%3A%2F%2Fwww.jpier.org%2FPIER%2Fpier40%2F01.0206091.Green.pdf&usg=AOvVaw3KI2NddabYy80mc2rx2-C8

I was also looking in the Ramo Fields and Waves book, and they had the reminder that TEM wave impedance can be derived by the static DC fields. So it reasons that the wire separation can go to infinity if the frequency goes to zero.

This, and that other post about quasi-TEM causing nulls for long lines, really makes me want to redo my whole education; dumber everyday.
• 0
Yes,it can be. Consider the reported Zo formula: increasing the distance from the ground increases the inductance per meter and reduces the capacitance per meter of the transmission line, differently than in free space where they are fixed by physics (space permeability and space permittivity ).So Zo may reach values even higher than 377 Ohm.
• 0
Is there a limit? Traveling wave antennas are tapered transmission lines. Maybe they have to be non-TEM lines? If you had a high impedance transmission line made of perfect conductor, with no dielectric loss, then there would be no loss. Those transmission line formulas do not account for radiation. So if a transmission line is always driven at a low enough frequency for TEM, I assume that means it can never radiate?
• 3
Thanks for the discussion!
I am going to answer my own question after thinking about this some more... impedance is defined as SQRT(L'/C').

if a microstrip is infinitely separated from its groundplane, the capacitance would be zero, and it would have infinite impedance! and infinitely useless.

This came about from playing with the wire-over-ground calculator, and observing what happens when the wire is a mile above ground.

https://www.microwaves101.com/calculators/874-wire-over-ground-calculator
• 0
Please consider that transmission lines theory leading to Zo formula is based on the assumption that no radiation occurs: that condition is only true when the distance between conductors is very smaller than the signal wavelength. Besides Zo function versus height is a logarithmic law, so increasing weakly at height increasing. For example, having 0.04 inch conductor diameter and εr=1 it is necessary a height of about 5.5 inch to have Zo = 377 Ohm…
• 3
Andrea

all good points! Any discussion of very high impedance transmission line should start with the caveat that for all practical purposes you cannot do much better than a few hundred ohms (for example, wirebond high above a ground plane) before the media falls apart and is useless.
• 0
The per-unit-length inductance can be raised with a spiral central conductor in a coax. Is that not used in some high impedance 'scope probes? Lumped-constant lines can be made whatever you want, such as distributed Y-amplifiers in old Tektronix valve oscilloscopes.
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